A Pizza Slice

ChefX showed ChefY his new pizza slice design. The design is a planar figure that can be drawn in the following way: - Draw a point $\mathsf{A}_0$ and two rays from this point such that the angle between them is $\alpha \lt \pi/2$. - Mark $N$ points $\mathsf{A}_1, \mathsf{A}_2, \mathsf{A}_3, \ldots, \mathsf{A}_N$ on one ray in this order ($\mathsf{A}_1$ is closest to $\mathsf{A}_0$). - Mark $N$ po